Nonlinear normal modes in electrodynamic systems: A nonperturbative approach

We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a non...

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Bibliographic Details
Published in:Journal of experimental and theoretical physics 2016-06, Vol.122 (6), p.995-1001
Main Authors: Kudrin, A. V., Kudrina, O. A., Petrov, E. Yu
Format: Article
Language:English
Subjects:
Analysis
ANALYTICAL SOLUTION
Atoms
CAVITY RESONATORS
Classical and Quantum Gravitation
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CYLINDRICAL CONFIGURATION
ELECTRODYNAMICS
Electromagnetism
Elementary Particles
FIELD EQUATIONS
Molecules
NONLINEAR PROBLEMS
Optics
OSCILLATIONS
Particle and Nuclear Physics
PERTURBATION THEORY
Physics
Physics and Astronomy
Quantum Field Theory
Relativity Theory
Solid State Physics
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Summary:We consider electromagnetic nonlinear normal modes in cylindrical cavity resonators filled with a nonlinear nondispersive medium. The key feature of the analysis is that exact analytic solutions of the nonlinear field equations are employed to study the mode properties in detail. Based on such a nonperturbative approach, we rigorously prove that the total energy of free nonlinear oscillations in a distributed conservative system, such as that considered in our work, can exactly coincide with the sum of energies of the normal modes of the system. This fact implies that the energy orthogonality property, which has so far been known to hold only for linear oscillations and fields, can also be observed in a nonlinear oscillatory system.
ISSN:1063-7761
1090-6509
DOI:10.1134/S1063776116060145